What Murdoch was doing was trying to channel the right wing's ardent support of Israel by challenging the left wing's more critical view of Israeli brinksmanship – particularly as Israel appears on the verge of another invasion of Gaza. In other words, or so Murdoch seemed to be close to saying, Jews are liberals, and so untrustworthy that they would even betray Israel.

From the biographer's point of view, this continues to be a curious and open-ended question: what does Murdoch really think about the Jews?

Murdoch's inopportune phrasing also goes to the larger question of the right's odd relationship to Israel, and its own feelings, more generally, about the Jews. Does being pro-Israel absolve you of your suspicion about Jews? Can you be an antisemite and still support Israel? (More provocatively: does Israel, in some sense, depend on the support of rightwing American antisemites?)

We are back in the weird nomenclature of antisemitism. What does "Jewish" as a modifier actually mean?

In this instance, I imagine Murdoch means the New York Times, which has been less than gung-ho about Israel charging into Gaza. I really can't think of what other press he might remotely have in mind as being "Jewish". (Various Jewish reporter pundits immediately claimed he was talking about them, but he seemed clearly to pin it on "owners" – which is the classic antisemitic construction. And, indeed, Murdoch apologized to the reporters who might have thought this – but not to the owners.)

To describe the Times this way is both quizzical, and we can assume, pointed. Because, as it happens, the Times isn't, per se, "Jewish". True, the Sulzbergers, who control the company, were once a prominent Jewish family. But the Times' chairman and publisher, Arthur Sulzberger, is half-Jewish (on his father's side) and was raised as an Episcopalian. Murdoch knows this full well. So what he is saying is something more like "Jewish-tainted press", which, all in all, seems more, not less, antisemitic.

Why would he say this?

In fair context, Murdoch comes from a generation (he's 81) and a place (Australia) where the word Jewish was often used in a way – a way that most often had an "other" implication – that it is not used now. And in private, Murdoch remains very much an unreconstructed person from his time and place.

Indeed, there is almost always a fluttering around Murdoch by his minders in an effort to clean up his retrograde-ness. (Once, when I interviewed his now 103-year-old mother, she made a retrograde remark about her son's Chinese wife that precipitated some serious crisis management in the company. Curiously, Murdoch's wife Wendi often uses the word "Jewish" in an atonal context – "You Jewish, right? I know you Jewish!" – that makes Murdoch's minders jump.) He may even become more retrograde to bedevil his minders.

But there is, among the people around, including the many Jews around him, a real and unresolved question about what Murdoch actually thinks about the Jews.

Gary Ginsberg, his long-time aide – part chief-of-staff; part PR consigliere – was often hurt and confounded by Murdoch's jibes, insensitivities, and humor (there was the Christmas every executive desk got a crèche by order of the boss). Once, with me, Murdoch got into a riff about Jewish groups and money: how they were good at tricking him out of his dough.

And yet, as soon as he focused his business attentions on the US and New York in the mid-seventies, he started to hire Jews as his closest advisers. His support for Israel has been absolute. Arguably, it is his support for Israel, and for neoconism in general (for many years, he owned and funded the losses of the Weekly Standard), that helped solidify rightwing support for Israel. (I was once at an Anti-Defamation League dinner where Rupert Murdoch presented Silvio Berlusconi an award for meritorious conduct with respect to the Jews.)

I think that Murdoch, a man not so much paranoid as he is realistic about his enemies, is parsing what he sees as "'good Jews" from "bad Jews". Jews are just another subset of the people who are for him or against him, who he either has to manage or isolate. Along with his open dislike of Muslims – once, he explained to me his theory about how Muslims often married close cousins, therefore depressing their general IQ – and his geopolitical views about world domination, supporting Israel, I believe, is a way to win the support of what he perceives as the good Jews. (That is, if you support him, you are a good Jew.)

There are the Jews in his tent pissing out, and there are the Jews who think they are better than him pissing in. (This is hardly the only way he parses his enemies: he does this in much more labyrinthine fashion when it comes to the Brits.) The New York Times represents the highest example of the Jews who believe they are better than him.

But I also wonder if there wasn't something else that slipped out in Murdoch's tweet. It is hard not to see the recent US election as a set of ethnic and demographic interest groups rising up to challenge the specifically white male right. From the point of view of the white male right, that might look awfully like the liberal Jewish dream come true. And curiously, it is now out there in the conversation. We openly parse the groups – ethnic, religious, and otherwise – who are for us or against us.

So, perhaps inevitably, this gets back to the Jews.

Murdoch really does try very hard to live in the modern world. But the truth is he is not very modern. Twitter, free of his minders, offers a direct line to who he is.